# Combining tree level LO and Loop Induced LO diagrams

Hey,

I need to generate g g -> Higgs -> ZZ -> 4 lepton events using SMEFT@NLO model for my analysis. Without EFT I was using: generate p p > h > l+ l- l+ l- [noborn=QCD] since it is a LI process. However using the SMEFT model will also include a tree level diagram so I can no longer do noborn=QCD. Is there a way that I can combine the tree level LO gg to Higgs and Loop induced LO gg to Higgs processes? I will also need to do reweighting on this later. Any suggestion would be helpful!

PS- I am studying dim6 operators that require me to generate the top loop explicitly. So I cannot for instance add a form factor using heft.

Thanks,

Jay Sandesara

## Question information

- Language:
- English Edit question

- Status:
- Solved

- Assignee:
- No assignee Edit question

- Solved by:
- Olivier Mattelaer

- Solved:
- 2020-03-03

- Last query:
- 2020-03-03

- Last reply:
- 2020-03-03

Is this what you want:

https:/

Cheers,

Olivier

> On 9 Feb 2020, at 14:17, Jay Sandesara <email address hidden> wrote:

>

> New question #688620 on MadGraph5_aMC@NLO:

> https:/

>

> Hey,

>

> I need to generate g g -> Higgs -> ZZ -> 4 lepton events using SMEFT@NLO model for my analysis. Without EFT I was using: generate p p > h > l+ l- l+ l- [noborn=QCD] since it is a LI process. However using the SMEFT model will also include a tree level diagram so I can no longer do noborn=QCD. Is there a way that I can combine the tree level LO gg to Higgs and Loop induced LO gg to Higgs processes? Any suggestion would be helpful!

>

> PS- I am studying dim6 operators that require me to generate the top loop explicitly. So I cannot for instance add a form factor using heft.

>

>

> Thanks,

> Jay Sandesara

>

> --

> You received this question notification because you are an answer

> contact for MadGraph5_aMC@NLO.

Jay Sandesara (jaysandesara) said : | #2 |

Hi,

Thanks for the suggestion. It is certainly helpful, but I would prefer to avoid doing this if possible since I am not confident enough about doing it correctly.

What if I generate the tree level process, reweight it to loop induced process using 'change process' in the reweight card, and then somehow combine the original weight and new weight to generate events.

I can do the first two parts, but is there an automated way of combining the original and reweighted sample to form a single unweighted .lhe file?

Thanks!

Jay Sandesara (jaysandesara) said : | #3 |

For instance, the lhe file for the new sample needs to include events from both samples (original and reweighted), but with a fraction equal to the ratio of their weights, with the events chosen using maybe a random number generator. And the new weights could be equal to the new cross section divided by the total number of events. Does this make sense? Is there a way to do this?

Hi Jay,

Let me be sure to understand what you want first.

If I understand you want to do the equivalent of this syntax:

generate g g > h > Z Z NP==1

add process g g > z z NP=0 [noborn=QCD]

which is mixing two samples assuming that they do not interfere at all.

To be honest I'm not 100% sure that this makes sense.

But if you want to do that, the easiest is to generate two unweighted sample of events:

one for

generate g g > h > Z Z NP==1

and one for

generate g g > z z NP=0 [noborn=QCD]

Then you compare the cross-section of the two samples and mix the samples according to the relative cross-section.

(and the new weight correspond to the sum of the cross-section up to normalization)

Cheers,

Olivier

Jay Sandesara (jaysandesara) said : | #5 |

Sorry for the incomplete information.

For the tree level processes, I am assuming I can do

generate p p > h > l+ l- l+ l- NP=2 [QCD]

The QCD part takes into account the tree^2 and tree*loop, which I need. However it doesnt generate the Loop^2 terms of the Standard model like Loop Induced processes. So I can reweight and do:

add process p p > h > l+ l- l+ l- NP=2 [noborn=QCD]

I think this will start the generation with Loop Induced as the LO and so Loop^2 is taken into account. Does what you suggest also apply here? With tree*loop (which is essential for my analysis).

You said it is 'mixing' two samples when I do reweighting. How does it mix?

Hi,

let me first explain mixing. If you use the following syntad:

generate p p > t t~

add process p p > Z Z

Then you will have a sample of events with both events containing top and Z.

The proportion of top is simply given by (sigma_tt/(sigma_tt + sigma_zz) (if we neglect statistical fluctuation obviously)

So for generating that sample, it is easy to

1) compute the two cross-sections

2) generate one sample for each (and ask the size of each sample in a smart way --i.e. proportional to their cross-section)

3) combine the two sample to get the correct ratio of events (use a RGN if you do not want to feeze that ratio to a fix value)

4) You typically randomise the order of the final sample, such that you are sure that you are allowed to only use the first X event without any bias.

So to go back to your specific case you can

1) generate p p > h > l+ l- l+ l- NP=2 [QCD]

Note that this also contains p p > 2l+ 2l- j (this is the real contribution)

2) generate a sample for g g > 2l+ 2l- NP=0 [ noborn=QCD]

Note that you can not have NP=2 for this process (the loop results will not be finite if you include NP=2)

3) You can use the mixing procedure described above (or just use those two sample independently in the analysis). Since you will use MC@NLO method for the first method, you will also have negative events, which makes the mixing a bit more complex than the simple procedure describe above.

So far I do not see any interest to use re-weighting method (or maybe again I do not understand what you are trying to include but If I do not then I'm really worried that you are trying to do something unphysical).

Cheers,

Olivier

Jay Sandesara (jaysandesara) said : | #7 |

Thanks for the answer!

Jay Sandesara (jaysandesara) said : | #8 |

Thanks Olivier Mattelaer, that solved my question.